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<div class="header">
  <div class="summary">
<a href="#nested-classes">Data Structures</a> &#124;
<a href="#func-members">Functions</a>  </div>
  <div class="headertitle"><div class="title">nc::polynomial Namespace Reference</div></div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="nested-classes" name="nested-classes"></a>
Data Structures</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classnc_1_1polynomial_1_1_poly1d.html">Poly1d</a></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ae4c5900df91c90ca21b3d177347e4d0f"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:ae4c5900df91c90ca21b3d177347e4d0f"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#ae4c5900df91c90ca21b3d177347e4d0f">chebyshev_t</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:ae4c5900df91c90ca21b3d177347e4d0f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afc70c903be3c216cf6215b76c89fecc0"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:afc70c903be3c216cf6215b76c89fecc0"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#afc70c903be3c216cf6215b76c89fecc0">chebyshev_t</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, dtype x)</td></tr>
<tr class="separator:afc70c903be3c216cf6215b76c89fecc0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6c9ffe24b0f67f4f28b4b9706a39fcf0"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a6c9ffe24b0f67f4f28b4b9706a39fcf0"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a6c9ffe24b0f67f4f28b4b9706a39fcf0">chebyshev_u</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:a6c9ffe24b0f67f4f28b4b9706a39fcf0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1e0f56b8366b1f83b48e30e7bb04c937"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a1e0f56b8366b1f83b48e30e7bb04c937"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a1e0f56b8366b1f83b48e30e7bb04c937">chebyshev_u</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, dtype x)</td></tr>
<tr class="separator:a1e0f56b8366b1f83b48e30e7bb04c937"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ade1c7e2792babf10bfaa60ff14156c12"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:ade1c7e2792babf10bfaa60ff14156c12"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#ade1c7e2792babf10bfaa60ff14156c12">hermite</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:ade1c7e2792babf10bfaa60ff14156c12"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aeea1ebbc592a6a8c533f2230fb0f6f10"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:aeea1ebbc592a6a8c533f2230fb0f6f10"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#aeea1ebbc592a6a8c533f2230fb0f6f10">hermite</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, dtype x)</td></tr>
<tr class="separator:aeea1ebbc592a6a8c533f2230fb0f6f10"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0b1fe04e7cc91218dfea6fb27e819f23"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a0b1fe04e7cc91218dfea6fb27e819f23"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a0b1fe04e7cc91218dfea6fb27e819f23">laguerre</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:a0b1fe04e7cc91218dfea6fb27e819f23"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa2c08952d8dfd2cccfbcd6da40b49f4f"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:aa2c08952d8dfd2cccfbcd6da40b49f4f"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#aa2c08952d8dfd2cccfbcd6da40b49f4f">laguerre</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, dtype x)</td></tr>
<tr class="separator:aa2c08952d8dfd2cccfbcd6da40b49f4f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1632161584f56e87ee9be46a43bdaadf"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a1632161584f56e87ee9be46a43bdaadf"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a1632161584f56e87ee9be46a43bdaadf">laguerre</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, <a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> m, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:a1632161584f56e87ee9be46a43bdaadf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad7fef1e52b0054b5894995ee1ed94340"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:ad7fef1e52b0054b5894995ee1ed94340"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#ad7fef1e52b0054b5894995ee1ed94340">laguerre</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, <a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> m, dtype x)</td></tr>
<tr class="separator:ad7fef1e52b0054b5894995ee1ed94340"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8ff11a959ecbfc4caf01f35cbc87420a"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a8ff11a959ecbfc4caf01f35cbc87420a"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a8ff11a959ecbfc4caf01f35cbc87420a">legendre_p</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> m, <a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:a8ff11a959ecbfc4caf01f35cbc87420a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6a68bde646dae6ffb484502d54e5c175"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a6a68bde646dae6ffb484502d54e5c175"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a6a68bde646dae6ffb484502d54e5c175">legendre_p</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> m, <a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, dtype x)</td></tr>
<tr class="separator:a6a68bde646dae6ffb484502d54e5c175"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9969335ebe0c26ff10af77007fcce5bc"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a9969335ebe0c26ff10af77007fcce5bc"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a9969335ebe0c26ff10af77007fcce5bc">legendre_p</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:a9969335ebe0c26ff10af77007fcce5bc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a567bdffcff63421b77a9dfae9cbdfc8a"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a567bdffcff63421b77a9dfae9cbdfc8a"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a567bdffcff63421b77a9dfae9cbdfc8a">legendre_p</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, dtype x)</td></tr>
<tr class="separator:a567bdffcff63421b77a9dfae9cbdfc8a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a00bc3047baef4182addac153f2b2c1a9"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a00bc3047baef4182addac153f2b2c1a9"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a00bc3047baef4182addac153f2b2c1a9">legendre_q</a> (<a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a> n, const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;inArrayX)</td></tr>
<tr class="separator:a00bc3047baef4182addac153f2b2c1a9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a78897e159974d6732b77759be2f2da13"><td class="memTemplParams" colspan="2">template&lt;typename dtype &gt; </td></tr>
<tr class="memitem:a78897e159974d6732b77759be2f2da13"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a78897e159974d6732b77759be2f2da13">legendre_q</a> (<a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a> n, dtype x)</td></tr>
<tr class="separator:a78897e159974d6732b77759be2f2da13"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af7a944bc738f9e7ca09d4669feeb03a3"><td class="memTemplParams" colspan="2">template&lt;typename dtype1 , typename dtype2 &gt; </td></tr>
<tr class="memitem:af7a944bc738f9e7ca09d4669feeb03a3"><td class="memTemplItemLeft" align="right" valign="top">std::complex&lt; double &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#af7a944bc738f9e7ca09d4669feeb03a3">spherical_harmonic</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, <a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a> m, dtype1 theta, dtype2 phi)</td></tr>
<tr class="separator:af7a944bc738f9e7ca09d4669feeb03a3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a583c30981b9547a90ad7c33edbe041c1"><td class="memTemplParams" colspan="2">template&lt;typename dtype1 , typename dtype2 &gt; </td></tr>
<tr class="memitem:a583c30981b9547a90ad7c33edbe041c1"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a583c30981b9547a90ad7c33edbe041c1">spherical_harmonic_i</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, <a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a> m, dtype1 theta, dtype2 phi)</td></tr>
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<tr class="memitem:a5ed971ca59899f372f28a53913796745"><td class="memTemplParams" colspan="2">template&lt;typename dtype1 , typename dtype2 &gt; </td></tr>
<tr class="memitem:a5ed971ca59899f372f28a53913796745"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacenc_1_1polynomial.html#a5ed971ca59899f372f28a53913796745">spherical_harmonic_r</a> (<a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> n, <a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a> m, dtype1 theta, dtype2 phi)</td></tr>
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</table>
<h2 class="groupheader">Function Documentation</h2>
<a id="ae4c5900df91c90ca21b3d177347e4d0f" name="ae4c5900df91c90ca21b3d177347e4d0f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae4c5900df91c90ca21b3d177347e4d0f">&#9670;&nbsp;</a></span>chebyshev_t() <span class="overload">[1/2]</span></h2>

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template&lt;typename dtype &gt; </div>
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          <td class="memname"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt; nc::polynomial::chebyshev_t </td>
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<p >Chebyshev Polynomial of the first kind. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the chebyshev polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#afc70c903be3c216cf6215b76c89fecc0">&#9670;&nbsp;</a></span>chebyshev_t() <span class="overload">[2/2]</span></h2>

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<p >Chebyshev Polynomial of the first kind. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the chebyshev polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6c9ffe24b0f67f4f28b4b9706a39fcf0">&#9670;&nbsp;</a></span>chebyshev_u() <span class="overload">[1/2]</span></h2>

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<p >Chebyshev Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the chebyshev polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1e0f56b8366b1f83b48e30e7bb04c937">&#9670;&nbsp;</a></span>chebyshev_u() <span class="overload">[2/2]</span></h2>

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<p >Chebyshev Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the chebyshev polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ade1c7e2792babf10bfaa60ff14156c12">&#9670;&nbsp;</a></span>hermite() <span class="overload">[1/2]</span></h2>

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<p >Hermite Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the hermite polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aeea1ebbc592a6a8c533f2230fb0f6f10">&#9670;&nbsp;</a></span>hermite() <span class="overload">[2/2]</span></h2>

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<p >Hermite Polynomial NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the hermite polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0b1fe04e7cc91218dfea6fb27e819f23">&#9670;&nbsp;</a></span>laguerre() <span class="overload">[1/4]</span></h2>

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<p >Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the leguerre polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa2c08952d8dfd2cccfbcd6da40b49f4f">&#9670;&nbsp;</a></span>laguerre() <span class="overload">[2/4]</span></h2>

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template&lt;typename dtype &gt; </div>
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          <td class="memname">double nc::polynomial::laguerre </td>
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<p >Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the leguerre polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a1632161584f56e87ee9be46a43bdaadf">&#9670;&nbsp;</a></span>laguerre() <span class="overload">[3/4]</span></h2>

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          <td class="memname"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt; nc::polynomial::laguerre </td>
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<p >Associated Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the leguerre polynomial </td></tr>
    <tr><td class="paramname">m</td><td>the degree of the legendre polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad7fef1e52b0054b5894995ee1ed94340">&#9670;&nbsp;</a></span>laguerre() <span class="overload">[4/4]</span></h2>

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          <td class="memname">double nc::polynomial::laguerre </td>
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<p >Associated Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the leguerre polynomial </td></tr>
    <tr><td class="paramname">m</td><td>the degree of the legendre polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8ff11a959ecbfc4caf01f35cbc87420a">&#9670;&nbsp;</a></span>legendre_p() <span class="overload">[1/4]</span></h2>

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          <td class="memname"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt; nc::polynomial::legendre_p </td>
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<p >Associated Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">m</td><td>the order of the legendre polynomial </td></tr>
    <tr><td class="paramname">n</td><td>the degree of the legendre polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value. Requires -1 &lt;= x &lt;= 1 </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6a68bde646dae6ffb484502d54e5c175">&#9670;&nbsp;</a></span>legendre_p() <span class="overload">[2/4]</span></h2>

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<p >Associated Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">m</td><td>the order of the legendre polynomial </td></tr>
    <tr><td class="paramname">n</td><td>the degree of the legendre polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value. Requires -1 &lt;= x &lt;= 1 </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9969335ebe0c26ff10af77007fcce5bc">&#9670;&nbsp;</a></span>legendre_p() <span class="overload">[3/4]</span></h2>

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          <td class="memname"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt; nc::polynomial::legendre_p </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;&#160;</td>
          <td class="paramname"><em>inArrayX</em>&#160;</td>
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<p >Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the degree of the legendre polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value. Requires -1 &lt;= x &lt;= 1 </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a567bdffcff63421b77a9dfae9cbdfc8a">&#9670;&nbsp;</a></span>legendre_p() <span class="overload">[4/4]</span></h2>

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          <td class="memname">double nc::polynomial::legendre_p </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
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          <td class="paramname"><em>x</em>&#160;</td>
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          <td></td>
          <td>)</td>
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<p >Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the degree of the legendre polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value. Requires -1 &lt;= x &lt;= 1 </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a00bc3047baef4182addac153f2b2c1a9">&#9670;&nbsp;</a></span>legendre_q() <span class="overload">[1/2]</span></h2>

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template&lt;typename dtype &gt; </div>
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          <td class="memname"><a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; double &gt; nc::polynomial::legendre_q </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classnc_1_1_nd_array.html">NdArray</a>&lt; dtype &gt; &amp;&#160;</td>
          <td class="paramname"><em>inArrayX</em>&#160;</td>
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<p >Legendre Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the legendre polynomial </td></tr>
    <tr><td class="paramname">inArrayX</td><td>the input value. Requires -1 &lt;= x &lt;= 1 </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a78897e159974d6732b77759be2f2da13">&#9670;&nbsp;</a></span>legendre_q() <span class="overload">[2/2]</span></h2>

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          <td class="memname">double nc::polynomial::legendre_q </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
        </tr>
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          <td class="paramkey"></td>
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          <td class="paramtype">dtype&#160;</td>
          <td class="paramname"><em>x</em>&#160;</td>
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          <td></td>
          <td>)</td>
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<p >Legendre Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>the order of the legendre polynomial </td></tr>
    <tr><td class="paramname">x</td><td>the input value. Requires -1 &lt;= x &lt;= 1 </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#af7a944bc738f9e7ca09d4669feeb03a3">&#9670;&nbsp;</a></span>spherical_harmonic()</h2>

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          <td class="memname">std::complex&lt; double &gt; nc::polynomial::spherical_harmonic </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
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        </tr>
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          <td class="paramname"><em>theta</em>, </td>
        </tr>
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          <td class="paramkey"></td>
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          <td class="paramtype">dtype2&#160;</td>
          <td class="paramname"><em>phi</em>&#160;</td>
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<p >Returns the value of the Spherical Harmonic Ynm(theta, phi). The spherical harmonics Ynm(theta, phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>order of the harmonic </td></tr>
    <tr><td class="paramname">m</td><td>degree of the harmonic </td></tr>
    <tr><td class="paramname">theta</td><td>Azimuthal (longitudinal) coordinate; must be in [0, 2*pi]. </td></tr>
    <tr><td class="paramname">phi</td><td>Polar (colatitudinal) coordinate; must be in [0, pi]. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a583c30981b9547a90ad7c33edbe041c1">&#9670;&nbsp;</a></span>spherical_harmonic_i()</h2>

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template&lt;typename dtype1 , typename dtype2 &gt; </div>
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          <td class="memname">double nc::polynomial::spherical_harmonic_i </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
        </tr>
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          <td class="paramkey"></td>
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          <td class="paramtype"><a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a>&#160;</td>
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          <td class="paramname"><em>theta</em>, </td>
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          <td class="paramtype">dtype2&#160;</td>
          <td class="paramname"><em>phi</em>&#160;</td>
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<p >Returns the imaginary part of the Spherical Harmonic Ynm(theta, phi). The spherical harmonics Ynm(theta, phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>order of the harmonic </td></tr>
    <tr><td class="paramname">m</td><td>degree of the harmonic </td></tr>
    <tr><td class="paramname">theta</td><td>Azimuthal (longitudinal) coordinate; must be in [0, 2*pi]. </td></tr>
    <tr><td class="paramname">phi</td><td>Polar (colatitudinal) coordinate; must be in [0, pi]. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a5ed971ca59899f372f28a53913796745">&#9670;&nbsp;</a></span>spherical_harmonic_r()</h2>

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          <td class="memname">double nc::polynomial::spherical_harmonic_r </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>&#160;</td>
          <td class="paramname"><em>n</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="namespacenc.html#a9386099a0fdc2bc9fb0dbfde5606584d">int32</a>&#160;</td>
          <td class="paramname"><em>m</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">dtype1&#160;</td>
          <td class="paramname"><em>theta</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">dtype2&#160;</td>
          <td class="paramname"><em>phi</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
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<p >Returns the real part of the Spherical Harmonic Ynm(theta, phi). The spherical harmonics Ynm(theta, phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. NOTE: Use of this function requires using the Boost includes.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">n</td><td>order of the harmonic </td></tr>
    <tr><td class="paramname">m</td><td>degree of the harmonic </td></tr>
    <tr><td class="paramname">theta</td><td>Azimuthal (longitudinal) coordinate; must be in [0, 2*pi]. </td></tr>
    <tr><td class="paramname">phi</td><td>Polar (colatitudinal) coordinate; must be in [0, pi]. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>

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